integral from-1 to 1 of 1/(1+y^2)

解答

\int_{- 1}^{1} \frac{1}{1 + y ^{2}} d y

\frac{π}{2}

十进制

1.57079 \dots

求解步骤

\int_{- 1}^{1} \frac{1}{1 + y ^{2}} d y

使用积分常见定则:

\int \frac{1}{1 + y ^{2}} d y = arctan (y)

= [arctan (y)]_{- 1}^{1}

带入上下限计算后得:

\frac{π}{2}

= \frac{π}{2}

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